Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0998.11030
Edixhoven, Bas
Rational elliptic curves are modular. (English)
[A] Séminaire Bourbaki. Volume 1999/2000. Exposés 865-879. Paris: Société Mathématique de France, Astérisque 276, 161-188, Exp. No. 871 (2002).

After the modularity of any semistable elliptic curve $E$ over the rationals had been proved by Wiles (and Taylor), it still was desirable to get rid of the semistability assumption. Step by step the class of elliptic curves known to be modular was enlarged, a program which was finally finished in [{\it C. Breuil}, {\it B. Conrad}, {\it F. Diamond}, and {\it R. Taylor}, J. Am. Math. Soc. 14, 843-939 (2001; Zbl 0982.11033)]. \par In the paper under review, the author describes Wiles' original strategy of proof and then outlines what had to be improved and how this could be done in order to get the full Shimura-Taniyama conjecture. He ends up by stating some more recent results on the modularity of Galois-representations.
[Stefan Kühnlein (Karlsruhe)]

MSC 2000:: *11G05 Elliptic curves over global fields
11F80 Galois properties
11F03 Modular and automorphic functions

Keywords: elliptic curves; modular curves; Galois representations; automorphic representations

Citations: Zbl 0982.11033; Zbl 0823.11029; Zbl 0823.11030

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]